Thursday, April 28, 2011

The Oppression Olympics is a game you play when you want to dismiss other people's problems because they aren't as bad as yours. Never mind that we can talk about multiple problems at once, or that smaller problems often have simpler solutions. People play this game all the time with asexuals. "Gays, lesbians, and bisexuals face a lot of hatred and discrimination in society. Asexuals just* get ignored and disbelieved. That may be annoying, but how does this concretely harm them?"

*This is not really true. Asexuals can also experience homophobia and other forms of hatred. But that's another topic.

People ask this same question of skeptics whenever they debunk things like homeopathy or astrology. Often, it's the case that these things do cause concrete harm, and we just aren't aware of it. There's a website called "What's the Harm?" which collects stories of harm caused by various kinds of pseudoscience and other nonsense.

Consider this an attempt to show, with evidence, that invisibility and erasure cause concrete harm. You know, if the anecdotes and informal polls aren't enough for you.

Assuming romantic couplings of two women are lesbian, or two men are gay, or a man and a woman are heterosexual.

Thinking bisexual people haven’t made up their minds, or are confused, or that it's merely a "phase".

Refusing to accept someone’s self-identification as bisexual if the person hasn’t had sex with both men and women.

Assuming bisexuals would be willing to “pass” as anything other than bisexual.

Thinking that bisexual people will have their rights when lesbian and gay people win theirs.

LGBT organizations failing to address the specific needs of bisexuals.

(Partly quoted, partly paraphrased from report. Not exhaustive.)

It's not true, by the way. That bisexuality is just a "phase". A 10-year study of women showed that they were more likely to adopt a bisexual label than relinquish one.

But what harm does that all cause? Surely bisexuals must have it better than gays and lesbians, since they can pass better, and get legally married. I mean, they're basically halfway straight, aren't they? Won't they get their rights when lesbian and gay people get theirs?

Nope. By many measures, bisexuals have it worse than gays and lesbians:

Bisexual women were more likely to be current smokers and acute drinkers.

Bisexual women in relationships with monosexual partners have an increased rate of domestic violence.

Bisexual women showed significantly higher rates of poor general health and frequent mental distress, even after controlling for confounding variables.

Bisexual women are more than twice as likely as lesbians to live in poverty (17.7% compared to 7.8%), and bisexual men are over 50% more likely to live in poverty than gay men (9.7% compared to 6.2%).

Gay men earn 2-3% less than straight men and lesbians 2.7% less, while bisexual men earn 10-15% less and bisexual women nearly 11% less.

(Partly quoted, partly paraphrased. Where bisexual women are specified, this is because it came from a study of only women. The same trend may or may not exist in bisexual men.)

Considering that bisexuals make up about half the LGB population and have some of the worst problems, it makes you wonder why we talk about about gay rights and not bisexual rights. Why do we talk about gay teen suicides and not bisexual teen suicides? Why do LGBT organizations invest so little, if any, of their resources on bisexual issues? Perhaps the issue of invisibility is too invisible (the irony!). People seem to think homophobia and discrimination are the only issues, and erasure you can just shrug off.

But now you know better. If homophobia were the only issue, you would expect bisexuals to fare the same or better than gays and lesbians by most measures. Instead, they do worse, and it is difficult to avoid the conclusion that this is partly due to invisibility and erasure. Or perhaps it's just the lack of community and institutional support (itself a result of invisibility).

Asexuals face homophobia less frequently than bisexuals, but I daresay they are even more invisible, and more erased. They certainly have less institutional support. I don't know of any studies which attempt to look at possible problems faced by asexuals, but I'm betting that they will find something. Studies differentiating bisexuals from gays/lesbians are the best proxy we have so far.

Note that this is not an attempt to play Oppression Olympics. Frankly, if I were to play, I would lose. Not just to trans people or to bisexuals, but to most other asexuals as well. Difficulties vary not just between groups but within groups, you see. This is merely an attempt to show that these issues exist.

Monday, April 25, 2011

The above chart shows the United States wealth distribution, alongside with what people think the wealth distribution is, and what people think it should be. It comes from a paper by Norton and Ariely earlier this year, and it's made the rounds in the news.

That's pretty interesting, but I always find myself wondering how to interpret this. Is the wealth distribution unfair, or are people just clueless about wealth distribution? Probably both. I feel pretty clueless about it myself.

To be honest, the very way the data is presented seems unintuitive to me. I mean, I'm a physicist, so what I consider "intuitive" is all out of whack. But seriously, the wealth owned by the top 20%? I have very little sense of what to expect from such a number. It has to be somewhere between 20% and 100%. 84% seems like too much, but what do I know?

If I were to pick a wealth distribution, I would start with a model, and from there calculate the percentage owned by the wealthiest 20%. So here's my model: wealth has a normal distribution on a log scale.* People who are one standard deviation above the mean own N times more than the median. People who are one standard deviation below own N times less than the median. N is a number that we can choose. For graphing purposes, I am choosing N=2.718 (Euler's number).

In the above graph, the median wealth is 1, meaning that half of people earn more than that and half earn less. But the mean wealth is actually more than that, since the distribution is skewed. And the most common amount of wealth (called the "mode") is about 40% of the median.

The next step is to translate this to the amount of wealth owned by the top 20%. So that's what I did for a few values of N:

(Note that though my plot has similar colors to the one at top, they aren't exactly the same since I split the top 20% into three groups.)

I showed N=6.5 because that's the number that seems to correspond to reality, according to Norton & Ariely. I showed N=2.718, because that's the number I would have guessed if I had never seen the real data. I showed N=1.5, because that's what strikes me as a "fair" distribution. In other words, I would think it was fair if people who are one standard deviation above the median own 50% more wealth. But in reality, they earn more than six times as much wealth.

I was surprised how similar my bar graph is to the one in Norton & Ariely. I'm quite sure that most people answering this poll have no understanding of normal distributions or log scales, and I was all set to conclude that people are clueless. I'm surprised to find that I agree with the popular opinion, because I think N=1.5 seems ideal.

Of course, the "ideal" value of N is completely arbitrary. What do you think is an ideal value of N? If you like, I can calculate the resulting wealth distribution.

*Some technical details: A normal distribution means that the probability density is exp[-y2/(2*log(N)2)]. But here, y is not the amount of wealth, but the log of the wealth. When I transform from a log scale to a linear scale, the probability density becomes exp[-log(x)2/(2*log(N)2)]*1/x, where x is the ratio of the wealth to the median wealth. This is the function I have plotted in the graph. This is, by the way, just about the simplest model imaginable.

Thursday, April 21, 2011

Last time I talked about my experience with one of the "needs" supposedly fulfilled by religion: spirituality. Now I will talk about another need: community.

I have a very strong need for community. I did not realize this until college, or perhaps I simply did not feel the need before.

The Catholicism I grew up in did not provide a community, at least not to me. I have memories of Sundays at church. We were always late to mass (sometimes my fault), and I did not talk to a single person there. I suppose there were just too many people, in the hundreds. The only social interaction occurred at a particular point in mass where everyone exchanged handshakes. "Peace be with you." "And also with you." And then there's the time when everyone holds hands while saying the Our Father. But that's it. It was more a ritual than real socializing.

And then there was CCD, which was like Sunday school, but on Wednesdays. My memories of this are very dim, since it was ages 5-10 (?), but I remember being introduced to the sacraments and doing lots of arts and crafts. I do not remember meeting any other kids this way. But then I didn't have any friends period at the time, so perhaps this was my fault and not CCD's fault.

Skipping ahead to college, one of the first things I encountered there were campus ministry organizations. Before classes even started, someone knocked on our dorm room door and offered us Red Vine (I am a sucker for licorice). Then she suggested going to someone's room where they would play games. So I did, along with my roommate. There were one or two dozen people there, and as we played Mafia I slowly figured out that the organizers were part of the Inter-Varsity Bruin Christian Fellowship. Some atheists might find it somewhat sinister that this group would "trick" us into coming, but I think it was genuine. We really did have fun playing games, and they were not pressuring anyone to become further involved.

By then, I no longer identified as Catholic, and my roommate was an apathetic Buddhist, but we were both impressed by the social opportunities it offered. I have to hand it to them, they knew how to organize a community. They had a variety of subspaces and types of activities. I didn't like the services because I don't like enthusiastic crowds or singing (not even getting into my disagreement with the sermons), but that was okay because there were plenty other things. I went to a few barbecues, a few house parties, and a few small group meetings, lots of dining hall dinners, and at one point a play. Some spaces made me uncomfortable as a non-Christian, so I just learned to avoid those things. Overall, I enjoyed the activities, and I liked the network of friends I made.

And yet it was definitely suboptimal for an atheist to be using a Christian space, so the next year I more or less stopped meeting new people in the group, and moved on to other things. One of those things was a student group called the Bruin Alliance of Skeptics and Secularists. Long-time readers know I was president of this group last year. This was great, for me anyways. I liked the absurd intellectual discussions, and I liked the collection of eccentric nerds I met. In all my experience with communities, I have never found one with as high a density of eccentricity as skeptical and atheist groups. And I like that. The down-side is that they're terribly organized (I especially felt this way when I was doing the organizing).

And then I became involved in the queer community. The queer community, I think is more... normal. They drink and party a lot, and they like pop culture. They have terrible taste in music, or maybe that's just me. Nonetheless, I am addicted to queer spaces.

What lessons can we derive from my personal story? It's hard to generalize, and I'm sure many details are just red herrings.

One lesson is that religion does not always provide for the needs that people say it does. I have never really felt much of a sense of Catholic community or Catholic culture. Catholicism is just boring. I have, on the other hand, found a wonderful community among atheists. But is this community for everyone, or is it only for eccentrics nerds? I have a hard time fighting this eccentric culture myself, because it's one of the things I personally enjoy.

The last lesson could be that we don't need to go to the atheist community to have community. The queer community is plenty secular, for instance. I'm betting most atheists who need a community simply find other communities that are not explicitly atheistic. Is there anything wrong with this, besides the fact that it makes atheists less visible? I honestly can't say there is.

Tuesday, April 19, 2011

To be honest, I'm not sure how much I can talk about intersectionality of asexuality and race. I'm quite sure that there must be some issues there, but because it's a mostly internet-based community, these issues are invisible to me. I find that issues of race really come to the forefront of any social movement at the conferences, but there are no asexual conferences.

However, I will make some slight adjustments to my talk to discuss general asexual intersectionality, if not specifically asexual/Asian intersectionality. This adjusted presentation will not appear online, but I'm sure the ideas will eventually percolate into my blog.

After this workshop, I'll have presented at more queer conferences than science conferences. I wonder if this means something is wrong with my academic life.

Monday, April 18, 2011

Now I want to show you an example of skepticism as applied to a queer issue. Skeptics will appreciate the article I found, but first I need to explain a lot of background.

Like any other community, the trans community has its internal politics and factions. What's more surprising is that there are some trans factions which are... I don't want to poison the well, so let's just say that they believe there is a hierarchy of trans people, and that they themselves belong at the top. I should emphasize that these factions are necessarily small because they're built on exclusivity.

The most extreme of these factions are the people with Harry Benjamin Syndrome (HBS). Named after a doctor who would probably not support them, HBS is an invented intersex condition causing the brain to develop as one sex, and the rest of the body to develop as the other sex. True HBS women conform to conventional gender expressions, down to the shopping, makeup, handbags, and painted nails, and any transwomen who fail to fit this are not real women. HBSers set themselves apart from "all the gay, lesbian, bisexual, crossdressers, transvestites, transgenders, genderqueers, autogynes, non-ops and others who claim to be afflicted with exactly the same condition that Harry found when in fact they have nothing but various degrees of mis-nurturing to account for their weird urges."* They even distance themselves from "transsexuals", since they believe the word has been tainted.

In short, HBSers feel that they are different from, and better than all people who fall under the transgender umbrella. And in fact, they could be right. About being different. Trans people are quite diverse, and it is likely that it is really a collection of different conditions with different etiologies. HBSers might even be right about belonging in a separate movement from transgender. After all, people who undergo complete transition do face some distinct issues.

But I doubt that HBS is quite as different as they suppose. And even if it were, this would not justify the way HBSers invalidate transgender people. And it does not justify, nor is it justified by, the pseudoscience they use to support their claims.

The article I found is called "The Science behind HBS", critically investigating the scientific arguments used in a book by HBS author Rose White.

White quotes an article by Zhou, Hofman, Gooren and Swaab from Nature 1997 (my emphasis):
"HBSS Harry Benjamin Syndrome Sufferers have strong feeling, often from childhood onwards, of having been born the wrong sex. - A female-sized BSTc was found in male-to-female HBS's -- the size was not influenced by sex hormones in adulthood and was independent of sexual orientation. - Investigation of genetics, gonads, genitalia or hormone levels have so far produced any results that explain HBS."

The paper is about statistical differences in the brains of people with gender dysphoria. Of course, when you actually look at the referenced paper, you find that the paper never referred to HBS, and was instead referring to transsexuals.

White has changed the text in order to make it look like these researchers support the use of the term Harry Benjamin Syndrome instead of the problematic word "transsexual". This is interesting, given that no official medical or psychiatric organisation anywhere in the world recognize the syndrome or use the label.

I find it interesting that they feel the need to go beyond quote mining into deliberate misquotation. But there's more.

The six transwomen Swaab & Co autopsied for their 1995 paper were not checked for HSB. They were dead and would not have been able to answer, anyway. All you can say is that they were M2F transwomen who had had sex reassignment surgery (or "sex affirmation surgery" to use White's term).

White agrees that a majority of those who transition are not HBS women. The chances are, therefore, that a majority of these six transwomen had been crossdreamers [ie autogynephiliacs] as well. If that is the case the paper could be said to have proved that crossdreaming has a biological basis.

And if that weren't enough, there's actually a paper that contradicts the claims of White. In White's view, only male-oriented transwomen could possibly be real women, but that's not what the studies show.

White does not mention a later paper by Swaab & Co, where they look a related part of the brain, the INAH3. In this study they did check for sexual orientation, and found no differences between gynephilic [female-oriented] transwomen and androphilic [male-oriented] transwomen:

Go ahead and read the rest of the post, and the rest ofthe series on the Crossdreamers blog. HBS is a pretty obscure issue, but a fascinating one, and I appreciate any smackdown as well-done as this.

Thursday, April 14, 2011

Recently I've been looking around for topics that combine critical thinking and queerness. It turns out there is a lot to talk about! Not just places where we can apply critical thinking to queer topics, but also lessons we can learn about critical thinking from queer discourse.

2) Breathe. Stay calm. Stay civil. Don’t assume that because someone criticized your action as transphobic that this means they’re saying you’re a bad person through and through. Your first reaction is probably from your defensiveness, not your brain.
...4) Don’t Make It About You. The best thing to do is apologize for what you said and move on. Resist your desire to shift the conversation into a lecture on How Against Transphobia You Are or How Accusations of Transphobia Are Just Silencing Tactics to Shut You Up. The subject of the conversation is probably not the many trans people you know, and your deep and abiding acceptance of their life choices.

5) Don’t Make It About Your Accuser. Just as you shouldn’t try to defend how you’re not transphobic, you should not also try to turn the criticism around and attack the person who accused you. Don’t tell them they’re trying to silence you – they’re not, they’re trying to tell you how your words and actions hurt them.
...

These are tips on how to avoid defensiveness in the situation where you are accused of transphobia (or racism, or sexism, or homophobia). But really, this is just a good critical thinking skill in general. I suppose it's pretty similar to open-mindedness, but "open-mindedness" is too vague to be a useful idea, while "avoiding defensiveness" is specific and direct.

The cognitive bias in play is people's belief in their own essential goodness. So if someone criticizes you, you think, "But I'm a good person! So I can't be wrong! You must be wrong!" But that's missing the point! It's not about whether you're a good person or not. It's about the ideas, and whether they are right or wrong. To put it bluntly, your own goodness as a person does not even come into the equation, though it may be a victim in the aftermath.

Personally, I think most people are good people. Call it my own cognitive bias. But good people can have wrong beliefs and do wrong things. And what are we to do about that? Whenever I criticize someone with the intent to persuade, and I have a smackdown argument, the number one thing on my mind is, "How do I say this without making them defensive?" There is no solution to this problem. And so, countless times, I have to watch people squirm around, combating their own defensiveness. I don't enjoy it. But it's pretty much all I can do. It's great when there is an occasional success.

So that's what I think about whenever someone criticizes me and I feel defensive. I channel my own experiences criticizing other people. I think about how much I hate it when other people react defensively, only thinking about the implications to their own moral character. I hate that this is an unavoidable risk. And then I try to avoid that same reaction in myself.

Monday, April 11, 2011

It's often said that religion fulfills a human need, and atheism fails to come up with a substitute. The crudest and stupidest way to put it is that atheists have a "god-shaped" hole in their hearts.

But there are more reasonable ways to put it such that most atheists would agree. Most religious people must be religious because they get something out of it, and it probably isn't a sense of intellectual integrity. So what are they getting out of it? Is it possible that people feel they won't get the same thing out of atheism? Is it possible that this biases people against atheism, even though, rationally speaking, it does not make an argument for God?

To organize my thoughts, I am splitting this into two parts. Each part will relate my own experience with a particular need that is supposedly fulfilled by religion. The first "need" is a sense of spirituality.

I don't have a need for spirituality. I have never had the need.

When I was Catholic, I never did get a sense of spirituality. Mass was an exercise in counting seconds away. Praying was a chore, one I could skip without consequence. I remember one time in my Jesuit high school we were all asked to relate a moment when we felt spiritual. I said I felt that way when I solved puzzles and got that "Aha!" moment. But privately I didn't think that was comparable, and I got that terrible feeling that you get when you've just shared something deep and personal about yourself, except it was a lie.

And then I left religion, and what did I find? Atheists are very emphatic about experiencing a sense of wonder at the universe. There is an entire atheist sub-movement called secular humanism with the explicit goal to fulfill this need for spirituality (and other needs usually fulfilled by religion). Carl Sagan and Albert Einstein are frequently invoked as people who both experienced and evoked awe and inspiration. The very first chapter in The God Delusion is called "A deeply religious non-believer", referring to how scientists often get mistaken for religious because they "touch the nerve-endings of transcendent wonder" and "[wax] ecstatic about nature and the universe."

I was very resentful of this emphasis on spirituality (I once blogged about it), but I was extremely hesitant to talk about it. I understood why spirituality was emphasized so much, and I didn't want to mess it up just because it made me feel left out. But in more recent years, because of my involvement in queer discourse, I had a realization. I realized that the feeling I get when people assume I need spirituality is the same feeling I get when people assume that I need a girlfriend. I will not explore this analogy, for it will surely fall apart, but it was the origin of my realization. From there I've been able clarify my thoughts and become more confident in speaking up.

There is a problem here, and it is not a problem within me. The problem is in my religious upbringing, in the atheist movement, and in the humanist movement. The problem is a failure to recognize human diversity.

I won't speak of other religions, but boy did my Catholic experience have this problem. It was filled with mandatory rituals and ceremonies. In all my religious education, it was constantly assumed that I felt religious experiences, or at least felt a need for them. There was much talk of god-shaped holes placed there by God. And what about people who did not feel this? Did God not bless them?

I've been told that I'm just too young. If that's the case, then why are young people forced to go through all the motions? Why not wait until they're older when, supposedly, they'll come to appreciate it?

As for the atheist and humanist movements, they have it wrong too. There is an overemphasis on spirituality, which is fine to some extent. It's used to counter the stereotype that atheists have no meaning in their life. But stereotypes cut both ways. They hurt the people who don't match the stereotype, and they hurt the people who are perceived as confirming the stereotype. It's too rarely that atheists discuss people who don't get this sense of spirituality. And this is what the silence says: people who don't care for spirituality have no meaning in their life.

What's worse is that the atheist and humanist version of spirituality is very narrow. It's all universe this, cosmos that, and sometimes a mention of meditation. What do I know, since I don't care for any kind of spirituality? But I bet there are a lot of people for whom this narrow version of spirituality is ineffective.

I've been told that there must be something in my experience which can be interpreted spiritually. Why is there such a need to pigeonhole my experiences when it feels so unnatural to me? And if spirituality is so broad, why do atheists only ever talk about a narrow version of spirituality based on physics and biology?

So, here's what we need to do as atheists. First, we need to recognize that not everyone needs the same things and gets the same things out of religion. I need no spirituality and found nothing spiritually unsatisfying in atheism. But that doesn't mean that everyone else will feel the same way as me. And there's no way that I can personally fix that. How can I help other people find spirituality in a secular worldview when I feel no need for it myself? Similarly, just because some atheist finds spirituality in the CMBR does not mean he should expect everyone to feel the same way about it. And if he wants to know what needs other people have, he needs to listen to other people.

Second, we need to get on religion's case for this same problem. If religion's defense is that it's fulfilling certain needs, then we should point out how religion is fulfilling them all wrong. Religion is blindly assuming that everyone has the same needs. Rituals only cater to a very narrow sense of spirituality. The talk of god-shaped holes is extremely marginalizing to many. And you know what happens to people who find religion spiritually unsatisfying? They leave, because it certainly isn't intellectually satisfying either.

Thursday, April 7, 2011

In this puzzle, the tiger can't swim (which is funny, because when I was looking for a tiger photo, I found pictures of tigers doing just that). Instead, the tiger will run along the edge of the lake, doing its best to catch you. The tiger runs four times as fast as you can swim.
You want to get out of the lake, but if the tiger is waiting for you when you reach the shore, then the tiger will seriously damage your ability to not die. Can you get out of the lake safely? How?
This puzzle is a classic, not original.

Monday, April 4, 2011

People who come out (hereinafter referred to as "outcomers") tend to fall into two categories: the experienced, and the novice.

That's the very first sentence of The Fine Art of Being Come Out To, and it contains one of the most important insights into what it means to come out. The first few times you come out, you are nervous, because you have no idea what kind of responses to expect. You are changing the way you present yourself, fighting the inertia of your own character. You may feel the need to sit someone down before confronting them and telling them your Big Secret.

Then you realize that there are a hundred other people in your life, and you don't have the time or energy to sit them all down one by one! You find out that most coming out experiences are anticlimactic. Soon you become really jaded, and lose track of who you're out to. Eventually, you only ever come out by off-hand references, and stop paying any attention to whether people pick them up. Or I should say, this all happened to me; I should stop pretending that I'm speaking for anyone else.

Hello, my name is miller, and I'm an experienced outcomer. I realize that I am speaking from a place of privilege. Not everyone has the opportunity to get where I am. And maybe some people don't even want to be where I am, which is their prerogative. But this is my experience.

In a way, I was already an experienced outcomer from the beginning. Several years previously, I had come out of the closet as atheist. When I discovered that I was asexual, I was extremely nervous and distressed, but I also knew what I had to do. I knew that I hated the closet. I knew who to come out to and how to find opportunity to do it. I knew what kinds of reactions to expect, and I knew most would be anticlimactic. I knew to try to let bad responses roll off my back. I knew that I was the kind of person who really benefited from a community after coming out.

Many months later, I determined that I was also gay. Since it was my third time around, I went from novice to jaded in record time.

As an experienced outcomer, I still have to come out all the time, but the game is changed. I'm always in this awkward position where I want to be out, but I don't want to make a big deal out of it. Sometimes, this means pretending that it is no big deal when it really is.

This is easy to do as gay. I generally don't ping people's gaydars, but it just comes up all the time without any effort on my part. For instance, people ask me what I do in my free time. I spend a lot of time hanging out at a queer-themed house. People ask me if I go to the city much. I don't anymore, but when I was dating, we went to several gay bars. What's more, I don't even need to talk to people to come out, because it's right there on my Facebook. The only people who will never know are my students, who I don't want knowing.

It's infinitely harder to come out as asexual. There is no A-dar. And it does come up in conversation, but not in a way that would be good to come out. For instance, people ask me if I think any of the guys are cute. This is the kind of situation where it would have good to be out already. I'm afraid of completely derailing a conversation. I'm afraid that a mere mention or off-hand reference would mislead more than enlighten. So I just say "no," which is true but misleading.

This is bad news for asexuals. No matter how privileged or empowered you are, there is a glass ceiling on being out. It always takes some effort to come out. If you want to be out to dozens of people, it all adds up. And if you spent that much effort on that many people, it would seem like it's all you ever talk about, perhaps because it is all you ever talk about.

And then I begin to question the value of coming out. Is it really worth all the silly drama? I need to be out as gay in order to have a nonzero chance of dating, but being out as asexual offers no such benefits. It's just, I feel unhappy when I'm closeted. I don't like the silent assumption that everyone has the same motivations. I don't like being ignored just because it is convenient. Is this irrational?

This is part of the reason I gravitate towards queer spaces. Usually they already have a baseline awareness of asexuality, so it's that much easier to just mention it. It's hard for me to keep track of who I'm out to, but the rule of thumb is that my straight friends know I'm gay, and my queer friends know I'm asexual. That's pretty much the best I can do, and I just learn to settle for it.

Saturday, April 2, 2011

As is always the case with these things, the best solution is to keep your colored hats in a safe place where logicians can't find them. But let's play along with them for a moment.

Strategy

1. If the other two logicians have opposite-colored hats, then abstain.
2. If the other two logicians have the same-colored hat, guess the color not seen.

If all three hats are the same color, then all three logicians will guess incorrectly. If two hats are one color, and the last hat is the second color, then that logician will guess correctly while the others abstain. Thus, the logicians win 75% of the time.

Proof of optimality

Remember that each hat is colored independently. Therefore, whenever a logician takes a guess, they have a 50% of getting it correct and 50% of getting incorrect. Suppose that the logicians have a predetermined strategy. There are 8 possible ways their hats can be colored. Among these 8 possibilities, there must be an equal number of correct and incorrect guesses.

For example, consider the strategy above. Here are the 8 possible colorings (R=red, B=blue) and the number of correct/incorrect guesses for each:

Here there are a total of 6 correct guesses and 6 incorrect guesses. It's all a matter of distributing those guesses in an optimal way. The best way to do it is to spread out the correct guesses and group together the incorrect guesses. There can be at most 3 incorrect guesses for a single possibility. Therefore 75% is the best you can do.

Adding more logicians
(Warning: advanced puzzle-solving ahead!)

If there are N logicians, we can prove that the best strategy can win no more than N/(N-1) probability. Of course, there is no guarantee that there exists any such strategy, and it may be that the best strategy is worse than that.

It turns out, though, that for 2k-1 logicians, we can devise such a strategy. But describing this strategy is difficult. I think the best way to describe it is by listing the "losing possibilities". A losing possibility is a hat-coloring which will result in all the logicians guessing incorrectly. For example, in the strategy I described for 3 logicians, the losing possibilities were BBB and RRR.

When each logician looks at the other hats' colors, she tries to determine if the hats may be colored like any of the losing possibilities. If not, then she abstains. If there's a chance that it's a losing possibility, then she bets against it by guessing the other color.

For 7 logicians, I need to pick 16 losing possibilities in such a way as to correctly distribute the correct guesses. Rather than listing out all 16, I will list 4. The rest of the losing possibilities can be found by taking bitwise XOR operations of other losing possibilities. (0=Blue, 1=Red)

1110000
1001001
0101010
0011100

This solution is not unique. Rather than proving it, I will simply assert that this wins with 7/8 probability.